3.1 Effect of angle of attack of aerofoil

The vorticity fields with streamlines are shown for $\alpha = 10^\circ $ in Fig. 4 and for $\alpha = 15^\circ $ in Fig. 5. The other parameters are the same as in Fig. 3 for $\alpha = 0^\circ $ ( $\varepsilon = 0.6$ and $\Gamma /{U_\infty }c = 0.55$ ). We note that the static stall angle is approximately 10° for the baseline aerofoil. In Fig. 4, there is already a weak separation over the baseline aerofoil in freestream ( ${U_\infty }t/c = 0$ ). As the incident vortex approaches and passes over the baseline aerofoil, the flow separation region has a similar size. There is even an indication of temporary reattachment at the last instant due to the downwash of the incident vortex. However, the mini-spoiler-induced flow separation is much more pronounced for $\alpha = 10^\circ $ . The flow separation region does not show significant variations as the incident vortex approaches and passes. Only after the vortex has passed the aerofoil, the instability of the shear layer becomes apparent, exhibiting a row of small vortices.

Figure 4. Comparison of vorticity fields between baseline aerofoil (left column) and with mini-spoiler (right column) for $\Gamma /{U_\infty }c = 0.55$ , $\varepsilon = 0.6$ , $\alpha = 10^\circ $ .

Figure 5. Comparison of vorticity fields between baseline aerofoil (left column) and with mini-spoiler (right column) for $\Gamma /{U_\infty }c = 0.55$ , $\varepsilon = 0.6$ , $\alpha = 15^\circ $ .

For the post-stall angle of attack of $\alpha = 15^\circ $ , the baseline aerofoil placed in freestream has massively separated flow (see top image in Fig. 5). In this figure, ${U_\infty }t/c = 0$ corresponds to the case of the aerofoil in steady freestream (with no gust). For all $U_{\infty}t/c$ , the phase-averaged flow is shown in Fig. 5. As the incident vortex approaches and passes there are significant changes in the separated flow. As the induced velocity of the approaching vortex increases, it initially reduces the separated region, causing deflection of the separated shear layer downwards at ${U_\infty }t/c = $ 2. At later times the induced velocity near the leading edge increases the flow angle and the separated region becomes larger, eventually causing the shedding of multiple vortices. The first LEV develops and sheds while forming a couple with the incident vortex followed by the shedding of a second LEV. In contrast, the separated region over the aerofoil with the mini-spoiler is remarkably stable until after the vortex has passed the aerofoil. This may be due to the fixed separation caused by the mini-spoiler in this case. Overall, the flow fields are more stable with the mini-spoiler and thus less lift variation may be expected during the interaction.

Qian et al. [Reference Qian, Wang and Gursul19] have shown that a positive lift peak is observed for all wings when the incident vortex is still upstream, regardless of the angle of attack and the offset distance, hence regardless of whether flow separation takes place or not. The positive peak occurs when the incident vortex reaches just upstream of the wing (roughly 30%c) at around ${U_\infty }t/c = $ 3.5. This distance corresponds to approximately five vortex core radii from the leading edge. The variation of the unsteady lift coefficient for the baseline aerofoil and with the mini-spoiler are shown in Fig. 6 at $\alpha = 0^\circ ,\;5^\circ ,\;10^\circ ,\;\;{\rm{and}}\;15^\circ $ , for $\Gamma /{U_\infty }c = 0.55$ and $\varepsilon = 0.6$ (corresponding to the cases in Figs. 3 to 5). (Note that parts (a) and (b) have the same scale, but the vertical axis is shifted according to the range of the values.) The positive peaks also occur around the same instant ${U_\infty }t/c = $ 3.5 with the mini-spoiler at all angles of attack. This confirms that the mini-spoiler induced separation region does not have a significant effect on the arrival time of the incident vortex. The maximum lift coefficient is reduced with the mini-spoiler, except for $\alpha = 0^\circ $ . The maximum lift reduction appears to be for the stall angle of $\alpha = 10^\circ $ . For each angle of attack, there is also a minimum lift, which may have a broader peak. The minimum lift is reached around ${U_\infty }t/c = $ 5. It is seen in Figs. 3–5 that at this instant the incident vortex is downstream of the trailing edge. The downwash of the incident vortex may also cause flow separation on the lower surface and a long recovery time for the unsteady lift [Reference Qian, Wang and Gursul19]. Nevertheless, the important quantity for loads attenuation is the positive peak lift force for a loaded wing.

Figure 6. Lift time history for baseline aerofoil and with mini-spoiler for $\Gamma /{U_\infty }c = 0.55$ , $\varepsilon = 0.6$ at: (a) $\alpha = 0^\circ $ & $5^\circ $ , (b) $\alpha = 10^\circ $ & $15^\circ $ .

The effect of the normalised offset distance $\varepsilon $ on the maximum lift for the baseline aerofoil has been discussed by Qian et al. [Reference Qian, Wang and Gursul19] in detail. The induced velocity in the cross-stream direction and the effective angle of attack both increase as the incident vortex approaches. If the interaction is assumed to be quasi-steady, a simple reduced order model [Reference Qian, Wang and Gursul19] predicts that the induced velocity by the incident vortex on the wing becomes maximum for the head-on collision ( $\varepsilon = 0$ ). The previous experiments and the data in Fig. 7 reveal that there is a slight asymmetry. Such asymmetric effects for the baseline aerofoil, which were also reported by Peng and Gregory [Reference Peng and Gregory18], can be explained by the accelerated flow on the wing surface for $\varepsilon \gt 0$ and decelerated flow on the lower surface for $\varepsilon \lt 0$ . The positive peak lift for the aerofoil with the mini-spoiler also exhibits similar variations to that of the baseline aerofoil. For all offset distances tested, there is an increase in the peak lift coefficient for $\alpha = 0^\circ $ , but a decrease for the pre-stall angle of attack of $\alpha = 5^\circ $ and the post-stall angle of attack of $\alpha = 15^\circ $ . In general, the lift reduction is better for the pre-stall angle of attack. In contrast, there is already stalled flow for the baseline aerofoil at the post-stall angle of attack. There is also some influence of the offset distance. For the post-stall angle of attack ( $\alpha = 15^\circ $ ), there is a degraded performance of the mini-spoiler for the strong vortex at small offset distances ( $\varepsilon = $ 0 to 0.2). For these conditions, the flow over the baseline aerofoil may be massively separated, making further lift reduction with the mini-spoiler small.

Figure 7. Peak coefficient of lift for the baseline aerofoil and with mini-spoiler for (a) $\alpha = 0^\circ $ , (b) $\alpha = 5^\circ $ , (c) $\alpha = 15^\circ $ .

The effectiveness of the mini-spoiler can be quantified as the change in the peak lift coefficient:

\begin{align*}\Delta {C_{L,{\rm{\;}}peak}} = {C_{L,{\rm{\;\;}}mini - spoiler,{\rm{\;\;}}peak}} - {C_{L,{\rm{\;\;}}baseline,{\rm{\;\;}}peak}}\end{align*}

The variation of the quantity $\Delta {C_{L,\;peak}}$ is shown as a function of aerofoil angle of attack in Fig. 8 for the weak vortex $\Gamma /{U_\infty }c = 0.55.$ We note that, as given in Section 2, the maximum tangential velocity V _max / ${U_\infty }$ is approximately 0.5 (the variation of the tangential velocity of the vortex as a function of distance from the centre is given by Qian et al. [Reference Qian, Wang and Gursul19]). The maximum tangential velocity can be considered as the maximum gust velocity in our case, i.e. ${V_{gust,\;max}}/{U_\infty }$ = 0.5. In Fig. 8 this case is shown as “travelling gust” with black solid circles. We also present the change in the lift coefficient in the freestream (in the absence of the gust). It is interesting that the change in the lift coefficient of the mini-spoiler on the aerofoil placed in steady freestream is almost identical to that when it is placed in the travelling gust. It may appear paradoxical that the mini-spoiler causes the same changes in the lift when in freestream and in the gust, even though the absolute values of the lift coefficient are significantly affected by the gust. We note that the positive peak of the lift force appears to be quasi-steady in nature as discussed above and modelled by Qian et al. [Reference Qian, Wang and Gursul19].

Figure 8. Variation of change in peak coefficient of lift $\Delta {C_{L,\;\;peak}}$ as a function of angle of attack for travelling vortical gust ( $\Gamma /{U_\infty }c = 0.55$ , $\varepsilon = 0.6$ ) and periodic plunging motion.

It will be interesting to compare the effectiveness of the spoiler in the travelling vortical gust and in the plunging motion previously studied [Reference Bull, Chiereghin, Cleaver and Gursul35]. The latter also represents the limiting case of infinite wavelength of a travelling transverse gust. For the case of the plunging aerofoil, the equivalent maximum gust velocity is taken as the maximum plunge velocity. The data calculated from Bull et al. [Reference Bull, Chiereghin, Cleaver and Gursul35] for various values of ${V_{gust,\;max}}/{U_\infty }$ are shown in Fig. 8. When the travelling gust is compared with the plunging aerofoil for the same value of ${V_{gust,\;max}}/{U_\infty }$ = 0.5, the changes in the lift coefficient are vastly different. The mini-spoiler does not appear to be effective over the whole range of angle of attack for the plunging aerofoil. (This can be attributed to the formation of the strong LEVs for both the baseline case and with the mini-spoiler, which makes the mini-spoiler inefficient.) However, for much lower values of plunge (or equivalently, gust) velocity, the effectiveness of the mini-spoiler on the plunging aerofoil increases and may even exceed the static effectiveness at the post-stall angle of attack (the mechanism of this superior performance was discussed by Bull et al. [Reference Bull, Chiereghin, Cleaver and Gursul35]). It is noted that, for the plunging aerofoil, the transverse velocity acts on the whole chord length of the aerofoil simultaneously. In contrast, the travelling gust in our experiments has the maximum gust velocity only for a small region around the vortex core (the core radius is about 0.06c for the travelling vortex). It appears that the length scale of the unsteadiness has significant influence on the effectiveness of the spoiler.

3.2 Effect of wing aspect ratio

The vorticity fields with streamlines at ${U_\infty }t/c = 3.5$ are compared for the loaded aerofoil in part (a) and for the finite unswept wing in part (b), with and without the mini-spoiler, in Fig. 9 for $\alpha = 5^\circ $ , $\Gamma /{U_\infty }c = 0.55$ , and $\varepsilon = 0.6$ . The PIV measurements were carried out in the mid-span plane for both the aerofoil and the wing. We note that the peak positive lift is observed around this instant for the aerofoil case. The flow fields for the aerofoil and the finite wing look very similar at this instant. The only noticeable difference is the streamwise location of the incident vortex. For the finite unswept wing, the incident vortex is slightly delayed. In Fig. 9, we see approximately the same shift in the streamwise location of the incident vortex between the upper row (aerofoil) and the lower row (finite wing). The shift/delay is roughly the same for the baseline case (left column) and with the spoiler (right column). This may be due to the smaller strength of the bound vortex of the finite wing compared to that of the aerofoil. The bound vortex, which has a clockwise direction, is expected to induce velocity on the incident vortex and accelerate it as the two become closer. We suggest that the delay of the incident vortex for the finite wing is due to the weaker bound vortex for the finite wing. This is consistent with the reduced effective angle of attack of the finite wing due to the aspect ratio correction.

Figure 9. Vorticity fields at ${U_\infty }t/c = 3.5$ for baseline aerofoil (left column) and with mini-spoiler (right column) for (a) aerofoil, (b) finite unswept wing, $\Gamma /{U_\infty }c = 0.55$ , $\varepsilon = 0.6$ , $\alpha = 5^\circ $ .

This is supported by the time history of the lift coefficient shown in Fig. 10. The variations of the lift coefficient for the aerofoil and the finite wing are similar, exhibiting positive peaks around the same time, but appear to be scaled down. Qian et al. [Reference Qian, Wang and Gursul19] presented a simple prediction of the maximum lift based on the lifting line theory for the steady aerodynamics. This quasi-steady approach provided a reasonable approximation. Figure 10 shows that, in the presence of the mini-tab, the variation of the lift coefficient with the mini-spoiler is also similar for the positive lift; however, negative lift peaks are observed, which may be due to the flow separation on the lower surface. Overall, the reduced positive lift for the finite wing is consistent with the reduced effective angle of attack.

Figure 10. Time history of lift coefficient of aerofoil and finite $\Lambda = 0^\circ $ wing, with and without mini-spoiler, for $\Gamma /{U_\infty }c = 0.55$ , $\varepsilon = 0.6$ at $\alpha = 5^\circ $ .

Figure 11. Change in lift coefficient $\Delta {C_{L,peak}}$ as a function of angle of attack for aerofoil and finite unswept wing in freestream and in gust, $\Gamma /{U_\infty }c = 0.55$ , $\varepsilon = 0.6$ .

The change in the maximum lift coefficient $\Delta {C_{L,peak}}$ for the aerofoil and the wing, in the freestream and in the travelling gust, is shown in Fig. 11 as a function of angle of attack for $\Gamma /{U_\infty }c = 0.55$ and $\varepsilon = 0.6$ . The variations of the change in the maximum lift coefficient are similar for the aerofoil and the wing, exhibiting the best lift reduction around the stall angle. The magnitudes for the finite wing appear to be smaller by a constant factor, which is related to the reduced effective angle of attack. We made a prediction for the change in the lift coefficient of the finite wing by using the data for the aerofoil and making a correction for the aspect ratio. We used the Prandtl’s lifting line theory with the assumption of an elliptical circulation variation:

\begin{align*} \frac{{{C_{L,3D}}}}{{{C_{L,2D}}}} = \frac{1}{{1 + \frac{{{a_0}}}{{\pi AR}}}} \end{align*}

and the slope of the lift coefficient was taken from the thin aerofoil theory (because of the non-linearity in the experiments shown in Fig. 2). The prediction is also shown in Fig. 11 with the dashed line, which reveals an excellent agreement with the measured data for the finite wing up to the stall angle. In this region, for both the aerofoil and the wing, the effectiveness of the mini-spoiler in the gust is slightly better than that in the freestream.

The volumetric velocity measurements were compared in Fig. 12 for the finite unswept wing at $\alpha = 10^\circ $ , with and without the mini-spoiler, $\Gamma /{U_\infty }c = 0.55$ and $\varepsilon = 0.6$ . At the stall angle of attack, the effectiveness of the mini-spoiler for the aerofoil and the wing differs most (see Fig. 11). We studied this angle of attack to investigate any interactions between the incident gust and the wing-tip vortex, and possible effect on the wing flow. In Fig. 12, the iso-surfaces of ${Q^*} = Q{c^2}/U_\infty ^2\; = 5$ are shown at ${U_\infty }t/c = 4$ and ${U_\infty }t/c = 4.5$ . The iso-surfaces are coloured by the spanwise vorticity ( $\omega c/{U_\infty }$ ). The incident vortex remains nearly two-dimensional as it travels over the wing. There is no evidence of any influence of the wingtip and tip vortex on the incident vortex for this offset distance. However, the effect of the wingtip is visible for the baseline wing case shown in Fig. 12(a) for ${U_\infty }t/c = 4$ . The leading-edge vortex shed from the wing is anchored at the wingtip, while the inboard part remains parallel to the leading edge but slightly downstream of the incident vortex. (We note similar shapes of the leading-edge vortex filaments on plunging wings at high reduced frequencies [Reference Son, Gao, Gursul, Cantwell, Wang and Sherwin45]) In contrast, for the wing with the mini-spoiler, there is no evidence of roll-p of a coherent LEV shedding at the same instant. Instead, the separated shear layer appears disorganised. In other words, the mini-spoiler prevents the rollup of the vortices. This feature is similar to that observed for wings plunging at not-so-high frequencies [Reference Bull, Chiereghin, Cleaver and Gursul35]. In Fig. 12(b) for ${U_\infty }t/c = 4.5,$ the leading-edge vortices just upstream and just downstream of the incident vortex are visible for the mini-tab case.

Figure 12. Isosurfaces of Q^*=5 coloured by z-vorticity ( $\omega c/{U_\infty }$ ) for baseline and with mini-spoiler for finite $\Lambda = 0^\circ $ wing at (a) ${U_\infty }t/c = 4$ ; (b) ${U_\infty }t/c = 4.5$ ; $\Gamma /{U_\infty }c = 0.55$ , $\varepsilon = 0.6$ , $\alpha = 10^\circ $ .

In Fig. 13 for ${U_\infty }t/c = 4$ , the iso-surfaces of ${Q^*} = Q{c^2}/U_\infty ^2\; = 5$ are coloured by the spanwise velocity $w/{U_\infty }$ (the positive velocity is towards the wingtip). There is no significant spanwise flow in the incident vortical gust during the interaction for both the baseline wing and with the mini-spoiler. There is some spanwise flow near the root towards the tip, but it becomes very weak as the wingtip region is approached. Outboard of the wingtip in the freestream there is a slight spanwise flow towards the wing root. However, in the leading-edge vortex (for the baseline wing) and in the separated shear flow (for the wing with the mini-spoiler), there is no sign of any spanwise flow.

Figure 13. Isosurfaces of Q^*=5 coloured by spanwise velocity ( $w/{U_\infty }$ ) for baseline finite $\Lambda = 0^\circ $ wing and with mini-spoiler at ${U_\infty }t/c = 4$ , for $\Gamma /{U_\infty }c = 0.55,$ $\varepsilon = 0.6$ , $\alpha = 10^\circ .$

3.3 Effect of wing sweep

Qian et al. [Reference Qian, Wang and Gursul19] have shown that the measured maximum lift coefficient can be estimated using the independence principle unless gust interaction produces a leading-edge vortex at post-stall angles of attack. Hence, volumetric velocimetry measurements were performed on the finite swept wing interacting with the strong vortex $\Gamma /{U_\infty }c = 1.07$ , at an offset distance $\varepsilon = 0.4$ and $\alpha = 15^\circ $ . Figures 14–16 present the iso-surfaces ${Q^*} = 5$ coloured by the spanwise vorticity during the vortex interaction at ${U_\infty }t/c\;$ = 3 (Fig. 14), ${U_\infty }t/c\;$ = 4 (Fig. 15), and ${U_\infty }t/c\;$ = 5 (Fig. 16), with the top views (top) and the three-dimensional views (bottom).

Figure 14. Isosurfaces of Q^*=5 coloured by z-vorticity ( $\omega c/{U_\infty }$ ) for baseline and with mini-spoiler for strong vortex $\Gamma /{U_\infty }c = 1.07$ , finite $\Lambda = 40^\circ $ wing, $\varepsilon = 0.4$ , $\alpha = 15^\circ $ at ${U_\infty }t/c = 3$ .

Figure 15. Isosurfaces of Q^*=5 coloured by z-vorticity ( $\omega c/{U_\infty }$ ) for baseline and with mini-spoiler for strong vortex $\Gamma /{U_\infty }c = 1.07$ , finite $\Lambda = 40^\circ $ wing, $\varepsilon = 0.4$ , $\alpha = 15^\circ $ at ${U_\infty }t/c = 4$ .

Figure 16. Isosurfaces of Q^*=5 coloured by z-vorticity ( $\omega c/{U_\infty }$ ) for baseline and with mini-spoiler for strong vortex $\Gamma /{U_\infty }c = 1.07$ , finite $\Lambda = 40^\circ $ wing, $\varepsilon = 0.4$ , $\alpha = 15^\circ $ at ${U_\infty }t/c = 5$ .

At ${U_\infty }t/c\;$ = 3, there is already flow separation from the wing, which forms a coherent leading-edge vortex. The angle of the axis of the leading-edge vortex is slightly larger than the wing sweep angle. However, with the mini-spoiler, the flow separation appears disorganised at this instant. When the incident vortex is roughly in the mid-span region at ${U_\infty }t/c$ = 4, the leading-edge vortex becomes nearly parallel to the wing leading edge for the baseline wing as it sheds and convects with the incident vortex. In contrast, with the mini-spoiler, the flow separation is organised as a leading-edge vortex that is nearly parallel to the incident vortex. At the final stage of ${U_\infty }t/c\;$ = 5, the incident vortex is highly three-dimensional and partly diffused for both cases. The inboard part of the incident vortex filament is already downstream of the wing and exhibits large three-dimensional distortion. Consequently, the leading-edge vortex is also three-dimensional and further away from the wing surface.

For the same case, the isosurfaces of ^Q* = 5, 35, 50, 70 in Fig. 17 are coloured by the spanwise velocity $w/{U_\infty }$ along the z-axis in the incident vortex and the velocity $w'/{U_\infty }$ along the wing sweep angle elsewhere. For both definitions of the velocity components, the positive velocity is towards the wingtip. There is negligible spanwise flow in the incident vortex upstream of the wing and during the interaction with the wing, for both the baseline wing and with the mini-spoiler. On the wing, there is strong flow along the axis of the leading-edge vortex, especially in the inboard part of the vortex filament, for the baseline wing. The vortex gradually becomes nearly parallel to the wing sweep. With the mini-spoiler, initially we do not observe strong flow along the wing. However, strong spanwise flow develops as the incident vortex moves over the wing, while becoming nearly parallel to the incident vortex.

Figure 17. Isosurfaces of Q^*=5, 35, 50, 70 coloured by velocity in z-direction ( $w/{U_\infty }$ ) and spanwise velocity ( $w'/{U_\infty }$ ) for baseline and with mini-spoiler for strong vortex $\Gamma /{U_\infty }c = 1.07$ , finite $\Lambda = 40^\circ $ wing, $\varepsilon = 0.4$ , $\alpha = 15^\circ $ .

For the unswept and the swept wing at the same angle of attack and in the same gust case as in Fig. 17, the time history of the lift coefficient is compared in Fig. 18 for the baseline case and with the mini-spoiler. Compared to the unswept wing case, the swept wing has smaller peak lift and slower increase and slower decrease of the wing lift as also demonstrated by [Reference Qian, Wang and Gursul19]. This is due to the delayed arrival time of the incident vortex as it approaches the outboard sections of the wing, resulting in asynchronous sectional lift and smaller total lift. Again, there is not much difference in the pattern of the lift coefficients and timings of the peaks. The mini-spoiler can reduce the maximum lift, whereas there is not much influence for the minimum (negative) lift.

Figure 18. For swept and unswept wings, time history of lift coefficient for baseline and with mini-spoiler, $\Gamma /{U_\infty }c = 1.07$ , finite wing $\Lambda = 40^\circ $ , $\varepsilon = 0.4$ , $\alpha = 15^\circ $ .

The effect of the wing sweep is illustrated in Fig. 19 by comparing the peak lift coefficients for the swept and the unswept wing cases at the same post-stall angle of attack ( $\alpha = 15^\circ $ ). It is concluded that the effectiveness of the mini-spoiler on the swept wing is not sensitive to either the strength of the incident vortex or the offset distance within the range tested. This may be due to the lessening effect of the asynchronous viscous interaction and flow separation for small offset distances. In contrast, for the unswept wing (Fig. 19(a)), the effectiveness exhibits some degradation for the interaction of the strong vortex with small offset, which implies that substantial flow separation is taking place simultaneously in the spanwise direction for the baseline case and making the spoiler ineffective for the already separated flow. On the other hand, the mini-spoiler effectiveness is generally better for the unswept wing except for the strongest vortex-wing interactions.

Figure 19. Peak lift coefficient for baseline and with mini-spoiler at $\alpha = 15^\circ $ , for (a) $\Lambda = 0^\circ $ , (b) $\Lambda = 40^\circ $ .